# 310-3141/03 – Mathematics IV (MIV)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor prof. RNDr. Radek Kučera, Ph.D. Subject version guarantor prof. RNDr. Radek Kučera, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
KRC76 Mgr. Jiří Krček
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+3

### Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions, Euler method for homogeneous systems of n equations for n functions. Integral calculus of functions of several independent variables: two-dimensional integrals, three-dimensional integrals, vector analysis, line integral of the first and the second kind, surface integral of the first and second kind. Infinite series: number series, series of functions, power series.

### Compulsory literature:

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990. ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Recommended literature:

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990, ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Way of continuous check of knowledge in the course of semester

Seminar Attending the seminar is required, only 20 % of missed lessons will be excused. It is also necessary to elaborate the home project in a form specified by the lecturer and a student is awarded 5 points for the project. Several tests will be carried out during the semester, a student can acquire up to 15 points. Examination The exam consists of two parts: I) Practical part - tests the ability of solving practical problems. (60 points is a maximum, but at least 20 points are necessary) II) Theoretical part - examines the understanding of the underlying theoretical concepts. (20 points is a maximum, but at least 5 points are necessary)

### E-learning

http://www.studopory.vsb.cz (in Czech language) http://lms.vsb.cz

### Other requirements

No more requirements are put on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Syllabus of lecture 1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions 2 Euler method for homogeneous systems of n equations for n functions 3 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2 4 Transformation - polar coordinates, geometrical and physical applications 5 Three-dimensional integrals on coordinate cube, on bounded subset of R3 6 Transformation - cylindrical and spherical coordinates, geometrical and physical applications 7 Vector analysis, gradient 8 Divergence, rotation 9 Line integral of the first and of the second kind 10 Green´s theorem, potential 11 Geometrical and physical applications 12 Infinite number series 13 Infinite series of functions, power series Syllabus of seminar 1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions 2 Euler method for homogeneous systems of n equations for n functions 3 Euler method for homogeneous systems of n equations for n functions, test 4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2 5 Transformation - polar coordinates 6 Geometrical and physical applications 7 Three-dimensional integrals on coordinate cube, on bounded subset of R3 8 Transformation - cylindrical and spherical coordinates 9 Geometrical and physical applications, test 10 Vector analysis, gradient 11 Divergence, rotation 12 Line integral of the first kind 13 Line integral of the second kind, test 14 Geometrical and physical applications

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 31
Practical part Written examination 60  25
Theoretical part Oral examination 20  5
Mandatory attendence parzicipation: 80%

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2020/2021 (N0715A270009) Industrial Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2020/2021 (N2301) Mechanical Engineering (2302T006) Energy Engineering P English Ostrava 1 Compulsory study plan
2020/2021 (N0715A270033) Applied Mechanics P Czech Ostrava 1 Compulsory study plan
2020/2021 (N0715A270022) Mechanical Engineering Technology P English Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P English Ostrava 1 Compulsory study plan
2019/2020 (N2301) Mechanical Engineering (2302T006) Energy Engineering P English Ostrava 1 Compulsory study plan
2019/2020 (N0715A270009) Industrial Engineering P English Ostrava 1 Compulsory study plan
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### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner